Question:

Find the antiderivative?

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gx = x² √(2x + 1)

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  1. ∫ x^2√(2x+1) dx

    ∫ x^2√(a+bx) dx = (2(8a^2-12abx+15b^2x^2)√(a+bx)^3) / 105b^3

    So, in this case, a=1 and b=2.  Plugging in gives

    (2(8-24x+60x^2)√(1+2x)^3) / 105(8) =

    (16-48x+120x^2)(√(1+2x)^3) / 840 =

    ((120x^2-48x+16)(1+2x)^(3/2)) / 840 + C

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